Flows on a cubic lattice
type: Item
instance of: scholarly article
title: Flows on a cubic lattice
zbMATH Open document ID: 1236.28012
DOI: 10.1134/S106456241104003X
author: M. L. Matdinov
published in: Doklady Mathematics
publication date: 2012-01-17T00:00:00Z
review text: The following is shown about measure transportation on \({\mathbb Z}^n\): Let \(M \subseteq {\mathbb Z}^n\) be a set. Suppose that there is some constant \(C \in {\mathbb R}\) such that, for every positive integer \(l\), every hypercube in \({\mathbb R}^n\) with sides of length \(l\) and parallel to the coordinate axes contains at most \(Cl^{n-1}\) points from \({\mathbb Z}^n \setminus M\). Then there exists a surjective map \(f:M \rightarrow {\mathbb Z}^n\) and a constant \(K\) such that \(\|f(m)-m\| \leq K\) for all \(m \in M\).
reviewed by: Christian Richter
Mathematics Subject Classification ID: 28D05
Mathematics Subject Classification ID: 28A35
Mathematics Subject Classification ID: 37A05
Mathematics Subject Classification ID: 52C07
Mathematics Subject Classification ID: 90B06
zbMATH DE Number: 5998435
zbMATH Keywords: cubic lattice
zbMATH Keywords: measure transportation
MaRDI profile type: Publication
cites work: Separated nets in Euclidean space and Jacobians of biLipschitz maps
cites work: Rectifying separated nets
cites work: Q3140233
cites work: Random complex zeroes. II. Perturbed lattice
description: scientific article; zbMATH DE number 5998435